JOURNAL OF TELECOMMUNICATIONS, VOLUME 5, ISSUE 1, OCTOBER 2010 12
Effects of Imperfect Power Control and Sectorization on the Capacity of Multiclass CDMA System with Beamforming Gunawan Wibisono and Lina Oktaviana Sari Abstract—Communications systems based on code division multiple access (CDMA) are growing fast this day. To support third generation technology (3G), CDMA has been expected to fulfill requirements of audio, data, and video services with higher system capacity. Audio, data and video services in CDMA systems can be viewed as multiclass CDMA system. In practice, the capacity of CDMA is limited by interferences, so that any reduction of the interference will directly cause capacity increases. Methods, such as sectorization and power control could reduce the interference. In this research, the impact of imperfect power control and imperfect sectorization to reverse-link user capacity of CDMA system based on signal to interference ratio ( SIR ) by using beamforming at mobile station (MS) transmitter and base station (BS) receiver will be analysed. It is shown from the results that the capacity of multiclass CDMA system decreases caused by the imperfect power control and imperfect sectorization. The system with sectorization using beamforming has large capacity of multiclass system than the system using beamforming without sectorization. The total addition of antenna beamforming elements at BS receiver and MS transmitter not always has large capacity of multiclass system, however depend on distribution of antenna beamforming elements at BS receiver and MS transmitter. The system with sectorization using beamforming has large capacity of multiclass system than the system with sectorization without beamforming. Optimum capacity of multiclass system achieved, when beamforming has even number of receive antenna elements Kr. Index Terms—beamforming, CDMA, imperfect power control, imperfect sectorization
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1 INTRODUCTION n code division multiple Access (CDMA) communication system, the system capacity is limited by interference, hence it has to be mitigated to increase the system capacity [1]-[3]. Several methods have been proposed to increase the system capacity, namely power control, sectorization, voice activity monitoring (VAM), beamforming (antena array) and multiuser detection. However in the implementation, the CDMA power control migh be imperfect due to the speed of adaptive power control, the dynamic range of the transmitter, and varying spatial distribution and propagation statistics [3]. These factors increase multiple access interference (MAI) so that the system capacity decreases. In sectorization, the cell is divided into several cells so that the number of interfering users decrease in accordance to the increase of the number of sectors. In reality, sectorization might be imperfect due to overlapping between sectors. This causes the BS to receive signals from neighboring sector so that the intercell interference increases and the system capacity decreases. The analysis of CDMA capacity in a reverse-link with sectorization, voice activity monitoring and power control is presented in [1]. Using sectorization, VAM and power control, the user capacity will increase. Reference [2] presents the system capacity analysis for reverse- and forward-links with
I
————————————————
imperfect power control. The numerical analysis shows that the imperfect power control in a reverse link will decrease the system capacity. On the contrary, in the forward link two power control schemes are used and the results show that a power-control scheme based on carrier-to-interference (CIR) will yield better results compared to distance-based scheme. Jie Zhou,Y.Onozato and U.Yamamoto [3] show the capacity and outage probability of the reverse-link in a CDMA system for macrocell and microcell celluar system with perfect/imperfect power control and sectorization have been presented. The results show that the user capacity will decrease as the power control and sectorization is increasingly imperfect. The analysis of the effects of imperfect power control on the reverse-link capacity of a CDMA system with fast power control and multipath fading is presented in [4]. Results show that the user capacity will decrease as the power control is increasingly imperfect. Jin Yu, Yu-Dong Yao, and Jinyun Zhang [5] show the capacity of a reverse-link CDMA using beamforming is analysed. Beamforming is a set of fixed array antenna used in the transmit and receive sides, assuming a power control based on signal to noise ration (SIR). In [5] it shown that beamforming increases the system capacity. The third generation cellular techonology CDMA (3G CDMA) is designetd to meet the requirements of audio, data and video services with large system capacity. To improve the system quality, sectorization is used. However imperfect sectorization will increase interference and decrease system
• Gunawan Wibisono with Department of Electrical Engineering, Faculty of Engineering University of Indonesia, Kampus Baru UI Depok 16424 INDONESIA. • Lina Oktaviana Sari with Department of Electrical Engineering. Jakarta State Politechnic, Kampus PNJ Depok 16424, INDONESIA. © 2010 JOT http://sites.google.com/site/journaloftelecommunications/
JOURNAL OF TELECOMMUNICATIONS, VOLUME 5, ISSUE 1, OCTOBER 2010 13
capacity. Therefore, to minimize the effects of interference and increase the system capacity, beamforming for sectorization is used [5]. In this research, the effect of imperfect power control and sectorization on the capacity of the reverse-link multiclass CDMA system using beamforming is analyzed mathematically. System capacity is defined as the maximum number of users per cell which is affected by the number of beamforming antenna elements, the number of sectors, the overlapping angles due to imperfect sectorization, imperfect power control, targeted SIR and CDMA processing gain. The use of beamforming in imperfect power control and sectorization condition is expected to increase the user capacity of the system. Beamforming is used in MS and BS assuming that the beamforming are uniformly excitead and equally spaced linear array.
5π
ω/2
The system model of a multiclass CDMA reverse link to be analyzed is shown in Fig. 1. The evaluated CDMA system is a macrocell in a homecell-BS surrounded by 6 cells in the first ring. BS is located in the center of the cell with path loss exponent of 4. Homecell-BS is divided into 3 sectors with effective beamwidth per sector of 120o. DESIRED SIGNAL
Fig 2.(a). Intracell interference, (b). 1 sector beamforming.
N −1
∑
Si
(1)
where Si is the power received by the i-th user from the BS.. Probability density factor ( pdf ) of Stra is closet o a log-normal distribution with mean, mtra and Standard deviation, σtra, as follows [3]: N −1 2 2 ∑ e2mi +σi 1 − eσ i (2) 2 σ tra = ln1 − i =1 2 N −1 2 e mi +σ i / 2 ∑ i =1
(
MS Intercell interference rm BS1 MS θ BS1 d MS
BS2 Rc
MS r0
MS
BS3
MS
MS
Intercell interference
HOMECELL BS BS0
MS
Intercell interference
MS
Intracell interference
MS
Intercell interference
MS MS
BS6
φ +1
1
−1 1
2.1 Intracell Interference Fig. 2 shows an interference in the system. In Fig. 2.(a), intracell interference in the BS homecell is caused by several MS located in the cell. The total intracell interference in the reverse link from an MS to BS0 is the total interference Si from N – 1 users serviced by the BS0.
1
π ∫ (1 − τ )(1 − (φ − τ ) )d τ , 1 f (φ ) = 1 ∫ dτ , π ( 1 − τ )(1 − (φ − τ ) ) 0, 2
There are 2 types of interferences in the system namely intercell interference and intracell interference. Intercell interference is due to an MS in a different cell, while intracell interference is caused by another MS in cell BS0.
(3)
where mi is the mean of each user. In perfect power control condition, the Standard deviation σi and σtra are 0 dB. If a sectorization with beamforming antennas in the homecell BS is done as shown in Fig. 2(b), the total inference from users Hill decrease. Fig 2(b) shows that φ 0 is the azimuth angle from MS0 to BS0 and φi is the azimuth angle from the MSi to BS0, these angles are evenly distributed from π to 5 π for 3 sectors. If φ = sin φi − sin φ0 , then the 6 6 pdf of φ for 3 sectors can be stated as [5]:
BS5
Fig. 1. System Model
)
2 2 N −1 mtra = ln∑ e mi +σ i / 2−σ tra / 2 i =1
MS
BS4
120o with antena
In imperfect power control condition, the total intracell interference is equal to a normal-distributed randrom variable, with a total intracell inteference Stra as follows [3]:
Intercell interference
MS
φi
i =1
SYSTEM MODEL
MS
6
φ0
ω/2
S tra = 2
π 6
2
φ −1
2
2
2
2
− 0.5 <φ < 0
0 ≤ φ < 0,5
others
The receive antenna gain from MS0 to MSi sectors can be stated as [5] :
Gr = Eφ0 ,φi [Gr (φi , φ0 )] =
sin2 (0.5K rπφ ) f (φ )dφ Kr2 sin2 (0.5πφ ) −0.5
(4) BS0 for 3
0.5
∫
(5)
The total intracell interference with sectorization without beamforming is given by :
ω 1 S sektor = Fz .S non− sektor = S non− sektor . + o z 360
(6)
JOURNAL OF TELECOMMUNICATIONS, VOLUME 5, ISSUE 1, OCTOBER 2010 14
where Snon-sektor = Stra is the total intracell interference with sectorization without beamforming. Using beamforming antenna, the total intracell interference for sectorization is
ω 1 S trs = + 360 z
N −1
∑
S i .G
(7)
r
i =1
Sectorization is done using antenna beamforming in BS0, if antenna beamforming is also used in MSi,j, then the total intercell interference with Sz in BS0, can be stated as : R
S z = Fz ∫ 0
µ
2π
(ξ − ξ j ) rm r 10 0 ∅ ξ 0 − ξ j , m 10 r0 0
∫ S r i
0
ρGt (θ u ,θ m )Gr (θ u , φ o )rm drm dθ
(12)
2.2 Intercell Interference All active users in the neighboring BS1 service area has the potential to interference with the homecell BS, as shown in Fig. 1. The received intercell inteferece in BS0 from i-th MS in BSj can be stated as [1] :
S ter
10ξ0 / 10 r µ = S i . µ . ξm / 10 j r0 10
(8)
where r0 is the distance of the i-th MS in the service area BSj to homecell BS and stated as [7]:
r0 = rm + d 2 + 2.rm d . cos θ
(9)
while rm is the closest distance between the i-th MS in BSj to its servicing BS [7], in Fig. 1, the servicing BS is BS1. d denotes the distance between BS0, µ is the path-loss exponent. ξ 0 and ξ j denote the shadowing process in the cells of BS0 and BSj. In Fig. 1, θ is the angle between MS to BS1 and BS0 to BS1. Using a system model inf Fig.1, where other than the homecell BS there are also 6 cells in the first tier surrounding the homecell BS, then the total intercell interference in BS0 from the i-th MS in BSj can be stated as [1]: R
Sj =
∫ 0
rm ∫0 S i r0
2π
µ
(ξ − ξ j ) r 10 0 ∅ ξ 0 − ξ j , m 10 r0
ρrm drm dθ
(10)
It is assumed that the number of users per cell is N and the users are evenly distributed in the cell, so that the user density ρ can be stated as [3] : 2N (11) ρ= 3 3R 2 If the number of users per sector is Nz and z is the number of sectorization, then N = z.Nz Fig. 3 shows the sectorization of homecell BS into 3 sectors with effective 120o beamwidth per sector. ,j Ms i
rm
rm
BSj
Ms i,j
BSj
θu
r0
d
MS0θ
0
d
r0
θm − π θu − π
i MS
Desired Signal BS0
θz
where
d sin θ 0 + r m sin θ m θ u = arctan d cos θ 0 + r m cos θ m
(13)
Gt(θu ,θm) and Gr(θu , φ 0 ) are the gain patterns of the transmit MS beamforming and receive BS. θu and θm are athe azimuth angles of the MSi,j and servicing BS0 and BSj. θ 0 is the azimuth angle of the BSj and BS0. Fig. 3 shows the angle notations of the transmit beamforming in MSi,j. When there are Kt beamforming transmit antenna elements in an MS, then by using (5), the transmit antenna gain in the direction of MSi,j to BS0 [5] is
sin( 0.5K t π (sin θ u − sin θ m )) Gt (θ u , θ m ) = K t sin(0.5π (sin θ u − sin θ m ))
2
(14a)
similarly, if there are Kr beamforming receive antenna elements in BS0 to receive singnals from MS0, then the receive antenna gain from MSi,j to BS0 can be stated as [5] G r (θ u , φ 0 ) =
sin(0.5K r π (sin θ u − sin φ 0 )) K r sin(0.5π (sin θ u − sin φ0 ))
2
(14b)
The average of total intercell interference with sectorization using beamforming Sz is given by
E[ S z
R
2π
] = F z E [ ∫ ∫ S i rm r0 0
r × ∅ ξ 0 − ξ j , m r0
µ
10
(ξ 0 − ξ j ) 10
0
ρ G t (θ u , θ m ) G r (θ u , φ o ) rm dr m d θ
(15)
]
Which can also be stated as :
E[S z ] = E[S i ]F (µ , σ )Fz N
(16)
with σ ln(10) 2 R 1 ω 2 F(µ,σ ).Fz = + exp ∫ z 360 3 3R2 10 0
2π
∫ 0
where r 10 µ ln(10) , x= log 10 0 − 2σ 2 2 10 2σ rm ∞ t2 1 Q(x ) = exp − dt dan ∫ 2π x 2 5π
1 Eφ0 [G r (θ u , φ 0 )] = 2π Fig 3. Sectorization of 3 sectors with beamforming
6
∫ G (θ π r
6
u
, φ 0 )dφ 0
µ
rm Gt (θu ,θm )Q(x)Eφ0 [Gr (θu ,φ0 )]rmdrmdθ r0
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2.3 The Capacity of Multiclass CDMA System In a CDMA system, SIR, and received Eb/Io must be larger or equivalent to a target γ x to maintain the quality of transmitted signal. Using beamforming in the transmit MS and receive BS [5], the Eb/Io for a singleclass CDMA is given by : Eb I0
Gx Si (17) = ≥γx 2 N x −1 x Fz ∑i =1 S i Eφ0 ,φi [G r (φ i , φ 0 ) + S z ] + η 0W 3 The factor 2/3 in the denominator is based on the assumption on square chip pulse. The subscript x denotes the traffic type. In the denominator in (16) there are intercell and intracell interference factors. η 0 denotes single sided white noise power spectrum density. Eb is equal to the target follows: γ x , so that Si can be stated usingSIz0 as x S z + 1.5η 0W (18) Si = A where 1.5G x (19) A= − ( N x − 1)Gr Fz
(
)
γx
The average of total intercell interference with sectorization using beamforming Sz for singleclass system can be stated as :
E [S z ] = E [S i ]F (µ , σ )Fz N x
(20a)
By subtituting Si in (18) to (20a), then (20a) can be written as
E[S z ] = E[S i ]F (µ , σ )Fz N x
=
1.5η 0WF (µ , σ )Fz N x 1.5G x
γx
(20b)
− ( N x − 1)Gr Fz − F (µ , σ )Fz N x
Where in (20b), E[Sz] has to be bigger than 0, because intereference always has a positive value , and therefore (20b) has to meet the following condition : (20c) 1.5η WF (µ , σ )F N E[S z ] =
0
1.5G x
γx
z
x
≥0
− ( N x − 1)G r Fz − F (µ , σ )Fz N x
By using (20c) and
F (µ , σ ) > 0 ,
Nx ≤
(
then the denominator in
1.5G x
γx
G r + F (µ , σ ) )Fz
Or similarly :
γx
(23)
(G r + F (µ , σ )) Fz
To support the third generation (3G) techonology, the chosen CDMA system is expected to cater the need of audio, data and video services with a large system capacity. The service comprising audio, data and video is referred as multiclass CDMA. In this research, the capacity of a multiclass CDMA system is derived. Multiclass CDMA system is a method to support the varying rates required by different users for different applications. In a multiclass CDMA system, a single code can be used for audio, data and video services with different processing gains. In this research, each of audio, data and video traffic uses different spreading code with processing gain Ga , Gd , and Gv. This way, the services with different rates can be accommodated with spreading sequence and varied processing gain. If the processing gain is normalized with G = Ga, then the normalized processing gain for audio, data and video services can be stated as ga, gd, dan gv. The total intercell interference from all traffic is S z = S za + S zd + S zv , therefore
E[ S z ] = E[S za ] + E[ S zd ] + E[ S zv ]
(24)
Three types of spreading sequence with different processing gains Gga, Ggd, dan Ggv are used to fulfill the requirements of different rates. To attain the target SIR (γa, γd, γv) for different services, and Pa, Pd, and Pv denote the received power of each service, given a beamforming in transmit MS and receiver BS, the Eb/Io for a multiclass CDMA system for each class is given by: Eb I0
Ga Pa = ≥γa 2 a (Fz ( (N a − 1)Pa Gr + N d Pd Gr + N v Pv Gr ) + S z ) + η 0W 3 Eb Gd Pd = ≥γd 2 I 0 d (Fz ( N a Pa Gr + ( N d − 1) Pd Gr + N v Pv Gr ) + S z ) + η 0W 3 Eb Gv Pv = ≥ γv 2 I 0 v (Fz ( N a Pa Gr + N d Pd Gr + ( N v − 1)Pv Gr ) + S z ) + η 0W 3
(25a)
(20c) can be written as : 1.5G x (21) − ( N x − 1)Gr Fz − F (µ , σ )Fz N x ≥ 0 γx By using (21), the user capacity N x for singleclass CDMA in a reverse-link with imperfect power control and sectorization can be stated as: G r Fz +
G r Fz + Nx =
1.5G x
(22)
where Sa = Paga, Sd = Pdgd ,and Sv = Pvgv respectively denote the normalized receive power for audio, data and video traffic merupakan normalisasi dari daya yang diterima untuk masing-masing trafik audio, data, dan video, so that (25a) can be rewritten as: Eb GS a = ≥γa I ( N − 1 ) S G F N S G N v S v Gr Fz 2 0 a a r z d d r Fz a + + + S z + η 0W 3 ga gd gv Eb GS d = ≥γd I 0 d 2 N a S a G r Fz + ( N d − 1) S d Gr Fz + N v S v G r Fz + S + η W z 0 3 ga gd gv
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Eb I0
GS v = ≥γv v 2 N a S a Gr Fz + N d S d Gr Fz + ( N v − 1) S v Gr F z + S + η W z 0 3 ga gd gv
The average of total intercell interference with sectorization using beamforming Sz for a multiclass system in (23) can be rewritten as :
(25b) In (25b), if Eb/Io for different traffic equals the target SIR for each traffic, then Sa, Sd, and Sv can be stated in Sz as follows : Sa =
S z + 1.5η 0W 1.5G 1 + N a N d g a G r Fz γ a G r Fz 1.5G + − G r Fz − 1.5G γa ga g gd 1 + a g d G r Fz γ d
E[ S z ] = E[ S za ] + E[ S zd ] + E[ S zv ] = E[S a ]
1.5G 1 + − N v g a G r Fz γ a gv 1 1.5G + g v G r Fz γ v
= { E [S a ]
(26a) 1.5G 1 + g a Gr F z γ a ( S z + 1.5η 0W ) 1 1.5G + g G r Fz γ d d Sd = 1.5G 1 + N a N d g a Gr Fz γ a N v Gr Fz 1.5G + − Gr Fz − − 1.5G g v γa ga g gd 1 + a g d Gr Fz γ d
=
1 1.5G + g a Gr Fz γ a 1 1.5G + g v Gr Fz γ v
}F (µ , σ )F z
E[S z ] N a N d Bd N v Bv + + C g a gd gv
+
1.5η 0W C
F (µ , σ )Fz
N a N d Bd N v Bv + + gd gv ga
F (µ , σ )Fz
N N B N B 1.5η 0W a + d d + v v F (µ , σ )Fz g g gv a d = N a N d Bd N v Bv F (µ , σ )Fz C − + + gd g v ga
N N B N B 1.5η 0W a + d d + v v F (µ , σ )Fz ga gd gv = N N B N B N N B N B Gr Fz 1.5G + − Gr Fz a + d d + v v − a + d d + v v γa ga gd gv ga gd gv ga
1 1.5G + g a Gr Fz γ a 1 1.5G + g v Gr Fz γ v
F (µ , σ )Fz
(30)
.(26c)
where in (30), E[Sz] must be larger than 0, because interference always has a positive value, so that (30) must meet the following condition:
Using a definition 1 1.5G + g a G r Fz γ a Bd = 1 1.5G + g d G r Fz γ d
(27a)
and 1 1.5G + g a Gr Fz γ a Bv = 1 1.5G + g v Gr Fz γ v
(27b)
then (26a), (26b) and (26c) can be rewritten as :
Sa =
Na N B N B + E [S a ] d d + E[S a ] v v ga gd gv
S + 1.5η 0W N a N d Bd N v Bv = E z g + g + g F (µ , σ )Fz C a d v
,(26b) 1.5G 1 + g a Gr F z γ a ( S z + 1.5η 0W ) 1 1.5G + g G r Fz γ v v Sv = 1.5G 1 + N a N d g a Gr Fz γ a N v Gr Fz 1.5G + − Gr Fz − − 1.5G g v γa ga g gd 1 + a g d Gr Fz γ d
Na N N F (µ , σ )Fz + E [S d ] d F (µ , σ )Fz + E[S v ] v F (µ , σ )F z ga gd gv
S z + 1.5η 0W C
(28a)
S d = Bd S a
(28b)
S v = Bv S a
(28c)
where N N B N B G F 1.5G C = r z + − G r Fz a + d d + v v (29) ga γa g g gv d a
N N B N B 1.5η 0W a + d d + v v F (µ , σ )Fz ga gd gv E [S z ] = N a N d B d N v Bv N a N d Bd N v Bv G r Fz 1.5G − + − G r Fz + + + + ga gd g v g a gd gv γa ga
(31) By using (31) and be stated as :
F (µ , σ )Fz
≥0
F (µ , σ ) > 0 , the denominator in (31) can
N N B N B N N B N B Gr Fz 1.5G + − Gr Fz a + d d + v v − a + d d + v v F(µ,σ )Fz ≥ 0 ga gd gv ga gd gv γa ga
(32)
Using (32), the capacity of multiclass CDMA system in a reverse link with imperfect power control and sectorization using beamforming antena can be stated as: G r Fz 1.5G + N a N d B d N v Bv ga γa + + = ga gd gv (F (µ , σ ) + Gr )Fz
(33a)
By using Bd and Bv in (27a) and (27b), then (33a) can be rewritten as follows:
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Na Nd + ga gd
1.5G 1 + + N v g a Fz Gr γ a gv 1 1.5G + g v Fz Gr γ v
1 1.5G + g a Fz G r γ a 1 1.5G + g d Fz G r γ d
Gr Fz 1.5G + γa ga = ( F ( µ , σ ) + Gr ) Fz
signals among users will increase. The increase of interference signals means there is a decrease in the Eb/I0 level, which can be used to represent SIR value. To attain the targeted SIR or the targeted signal quality, the system capacity will decrease.
(33b)
120
So that the capacity of a multiclass CDMA system can be stated as:
ω = 0o
100
Capacity Of Multiclass System
ω=10o
Na 1 1.5G 1 1.5G Nd + + + ga gd FzGr γ d gv FzGr γ v gd
1 1.5G 1 1.5G + + ga Fz Grγ a gv Fz Grγ v 1 1.5G 1 1.5G 1 1.5G + + Gr Fz + ga Fz Gr γ a gd Fz Grγ d gv FzGrγ v Nv 1 1.5G 1 1.5G + = + + gv ga Fz Grγ a gd FzGrγ d (F(µ,σ)Fz +Gr Fz )
(33c)
3
ω=20o
80
60
z =1 Without sector
z =3sectors
40
20
0 0
RESULT AND ANALYSIS
TABLE 1 PARAMETER USED Na: User Audio
Spreading bandwidth (W) [5] Processing Gain[5] Target SIR [5] Power Control Factor σ(dB) Propagation Constant (μ) Receive Antenna Elements[5]; Transmit antenna elements[5]; Overlap angle (˚) Number of sectors (z)[3]
Nd: User Data
Nv: User Video
4.096 Mbps Ga =128 / ga =1 γa= 5 dB
2
3
4
5
6
7
8
Power Control Factor σ (dB)
The parameters used in measuring the capacity of audio, ata and video users in a multicalss system is given in Table 1.
Parameter
1
Gd =64/ gd = 0.5 γd =10 dB
Gv=32 / gv=0.25 γv= 7 dB
0,2,4,6,8[1] 4[1] 1-9 1-4 0;5;10;15[3];20 3
4.1 EFFECT POWER CONTROL AND SECTORIZATION 4.1.1 Capacity of Multiclass System Fig. 1 shows the capacity of a multiclass system under the effects of power control. The capacity of a multiclass system with sectorization z = 3 is compared to a system without sectorization. In Fig. 1 it is shown that the capacity of the system with and without sectorization will decrease in accordance to the decrease of power control effects. As the power control grows increasingly imperfect the interference
Fig. 1 Capacity of a multiclass sytem as a function of power control, for z = 1 and z = 3 ,
ω = 0 o , ω = 10 o , ω = 20o .
In Fig. 1 it is shown that by using sectorization with z = 3 o and the sectorization is perfect ( ω = 0 ), the system capacity will increase compared to a system without sectorization. This is due to the fact that a user in a multiclass system is connected only by a BS which sector antenna is facing that particular user. As a result a particular user will receive interference signals from users in the same sector. If there o o exist overlapping angles ω = 10 and ω = 20 between sectors, it means the sectorization is growing more imperfect and as shown in Fig. 1, the capacity will decrease compared to a system with perfect sectorization. This happens as a user receives interference signals from users in other sectors. However in Fig. 1 it is shown that the capacity for a system o o with overlapping angles of ω = 10 , ω = 20 between sectors is still larger compared to system without sectorization.
4.1.2
Capacity of Audio, Data and Video Users in A Multiclass System. The effects of power control and sectorization on the capacity of audio, data and video users for a multiclass system is depicted in Fig. 2 to 4. In each of these figures, the effect of power control is analysed for σ = 0 dB which indicates perfect power control. For imperfect power control, σ = 2 dB to σ = 4 dB is used. In each of these figures, sectorization is done using z = 3, with overlapping angle between sectors ω = 0oo which indicates perfect o sectorization, and ω = 10 and ω = 20 for increasingly imperfect sectorization.
JOURNAL OF TELECOMMUNICATIONS, VOLUME 5, ISSUE 1, OCTOBER 2010 18
the fact that several slots for data users are used for video users.
120
30
80
ω=0o
σ =0dB
25
ω =10o 60
User Data Capacity
User Audio Capacity
ω = 0o
σ = 0dB
100
ω = 20o 40
σ = 2dB 20
20
ω=10o
15
ω=20o
10
σ = 4dB 0 0
5
σ =2dB
10
15
20
25
5
30
User Data Capacity σ =4dB
Fig. 2 Capacity of audio users a function of data users in a multiclass system with sectorization and power control.
0 0
2
4
6
8
10
12
14
16
18
20
User Video Capacity
Fig. 2 to 4 show that the capacity of audio, data and video users will decrease in accordance to increasingly imperfect power control. These figures also show that as the sectorization is increasingly imperfect, the capacity of audio, data and video users will decrease. 120
σ = 0dB
ω = 0o
User Audio Capacity
100
80
ω =10o
Fig.4 Capacity of data users as a function of the capacity of video users in a multiclass system with sectorization and power control.
In Fig. 2 to Fig. 4, it can be observed that the audio users capacity is larger than that of data users and video users capacity, and the user data capacity is larger than the video user capacity. This is due to the fact that the audio processing gain is larger than the data and video processing gains, and the data processing gain is larger than the video processing gain, where small processing gain has high bit rate. A high bit rate requires high level of power, as the power requirement is directly proportional to bit rate, so that the interference signal increases and system capacity decrease.
60
ω = 20o
4.2 40
σ = 2dB 20
2
POWER
OF
CONTROL
AND
4.2.1 Capacity of Multiclass System with the Increase of Receive Antenna Elements.
σ = 4dB 0 0
EFFECTS
SECTORIZATION WITH BEAMFORMING.
4
6
8
10
12
14
16
18
20
450
User Video Capacity
Fig. 2 shows that for both imperfect and perfect power control and sectorization conditions, the capacity of audio users will decrease in accordance with the increase of user data capacity, assuming that the number of video users is constant. This happens because several slots of the audio users are used for data users. In Fig. 3, it is shown that the capacity of audio users as a function of video users also decreases as the number of video users increase, assuming that the number of data users is constant. This happens because several slots of the audio users are used for video users. Fig. 4 shows the capacity of data users as a function of video users, assuming the number of audio users is constant. From Fig. 4 it is observed that the capacity of data users decreases as the video users capacity increases, this is due to
400
Capacity Of Multiclass System
Fig.3 Capacity of audio users a function of video users in a multiclass system with sectorization and power control.
350 300
z = 3 Sector
σ = 0dB z = 1(Without Sector)
σ = 2dB σ = 4dB 250 200 150 100 50 0 1
2
3
4
5
6
7
8
9
Receive Antenna Elements Kr
Fig 5. Capacity of multiclass system as a function of receive antenna elements Kr, for Kt =1, with power control and sectorization.
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4.2.2
Capacity a Multiclass System for Distributed Antenna Elements
Fig. 6 shows the effects of increasingly imperfect sectorization on the capacity of a multiclass system with o increasing inter-sector overlapping angle from ω = 0 to o ω = 20 and the effect of imperfect power control with σ = 8 dB. The multiclass system capacity is also affected by the increased number of receive antenna elements in the MS Kt = 1,2. As can be observed in Fig. 6, the increase of transmit antenna elements in MS to Kt = 2 will yield higher capacity of the multiclass system compared to the use of Kt = 1. This is due to the fact the increased receive antenna elements allows for modifying transmit beam patterns to minimize the interference towards unwanted receivers. In Fig. 6 it is also shown that the use of Kr = 3, Kt = 2 yields higher multiclass system capacity compared to the used of Kr = 5, Kt = 1 and Kr = 7, Kt = 1. This emphasizes the importante of antenna elements distribution in the receive BS and transmit MS to yield a maximum system capacity. One of the disadvantages of the use of beamforming antenna is the increasing requirements of hardware/software to control the number of antenna elements. Therefore, the distribution of antenna elements in the receive BS and transmit MS is important as it forms a solution to pinpoint the number of antenna elements hended to yield a maximum system capacity.
250
Capacity of Multiclass System
The effect of increasing Kr in multiclass system capacity without sectorization is shown by using z = 1 while that with o perfect sectorization uses z = 3, ω = 0 . In Fig. 6 it is shown that the multiclass system capacity with beamforming sectorization is larger compared to a system without sectorization. For increasingly imperfect power control with σ = 4 dB a higher capacity increase will occur in accordance with the increase of receive antenna elements Kr compared to perfect power control σ = 0 dB with one receiver in BS. This is due to the fact that increasing beamforming receive antenna elements in BS for a reverse-link transmission allows the combination of signals from the antenna elements to form a movable beam patterns capable of adjusting to the movements of MS. This allows the system antenna to focus radio frequency to a particular MS and minimize the effects of interference so that the system capacity is increased.
300
Kr=7 Kt=2
200
Kr=5 150
100
Kr=3
Kt=1
50
0 0
2
4
6
8
10
12
14
16
18
20
Overlap Angle ω
Fig. 6 Capacity of a multiclass system as a function of overlapping angle, for Kt =1;2, Kr = 3;5;7, power control wtih 3.
σ = 8 dB and sectorization =
Fig. 7 shows the distribution of antenna elements in receive BS and transmit MS. If the total number of antenna elements in receive BS and transmit MS is Kr + Kt = 4;6;8;10, then the maximum multiclass system capacity is attained when Kt = 2. This is due to the fact that the total gain of the antenna elements in receive BS and transmit MS is lower if Kt = 2 compared to Kt = 1;3;4 , so that the interference yielded is also lower and in turn the capacity yielded is higher. In Fig. 7 it is shown that Kr = 5, Kt = 3 and Kr = 4, Kt = 4 will yield higher system capacity compared to Kr = 7, Kt = 1 and lower capacity compared to Kr = 6, Kt = 2. In Fig. 7 it is also shown that Kr + Kt = 6, for Kr = 4, Kt = 2 yields a higher system capacity compared to Kr + Kt = 8, for Kr = 7, Kt = 1. This shows that the increase of total antenna elements in receive BS and the antenna elements in transmit MS does not always increase the capacity of a multiclass system. Instead, the capacity increase is affected by the distribution of the elements in the receive BS and transmit MS.
350
Kr+Kt=10
Capacity Of Multiclass System
Fig. 5 shows the effects of increasing receive beamforming antenna elements Kr on the capacity of a multiclass system. The number of antenna elements Kr in BS increases from 1, 3, 5, 7 to 9 while the number of transmit antenna elements in MS Kt = 1. The effect of power control on system capacity is analysed for σ = 0 dB, σ = 2 dB, and σ = 4 dB.
300
250
Kr+Kt=8
200
ω = 0o
Kr+Kt=6
ω = 20o
150
Kr+Kt=4 100
ω = 0o ω = 20o
50
0 1
2
3
4
5
6
7
8
9
Receive Antenna Elemen Kr Fig.7 Effect of antenna elements distribution on the multiclass system capacity, for power control with
σ = 8 dB and sectorization z = 3.
JOURNAL OF TELECOMMUNICATIONS, VOLUME 5, ISSUE 1, OCTOBER 2010 20
With increased overlap angles between each sector, in Fig 6 an 7 it is observed that the capacity of a multiclass system for all beamforming antenna elements will decrease.
250
Kt = 2, Kr = 4
User Audio Capacity
4.2.3 Capacity of Audio, Data and Video Users In Multiclass System with Beamforming. Fig. 8 to 10 show the effects of power control and sectorization on the capacity of audio, data and video users in a multiclass system using beamforming antenna. In each of
ω =20o
150
overlaping angle between each sectors
ω=0
which
o
indicates perfect sectorization, and ω = 20 indicating imperfect sectorization. The effect of beamforming antenna for sectorization can be observed by comparing the capacity of the audio, data and video users for Kt = 2, Kr = 2;4.
250 Kt =2,Kr =4
ω=0o
User Audio Capacity
200
ω=20o 150
σ =0dB
100
50
σ =8dB
Kt = 2,Kr =2
0 0
10
20
30
40
50
σ = 0dB
σ =8dB
100
tose figures the power control uses σ = 0 dB whic indicates perfect power control. The effect of imperfect power control is shown with σ = 8 dB. In each of those figures, a sectorization of z = 3 is done using beamforming antenna with o
ω = 0o
200
50 Kt = 2, Kr = 2 0 0
5
10
15
20
25
30
35
40
User Video Capacity
Fig.9 Capacity of audio users a function of the capacity of video users in a multiclass system for Kt = 2, Kr = 2;4, with sectorization and power control.
In Fig. 8 it is shown that for a system with power control and both perfect and imperfect sectorizations, the capacity of audio users will decrease in accordance to the increase of the capacity of the data users, under the assumption that the the number of video users remain the same. This is due to the fact that several slots for audio users are used for the data users. In Fig. 9, it is shown that the capacity of the audio users as a function of the capacity of the video users also decreases in accordance to the increase of video users, if the number of data users is assumed to be constant. This is due to the fact that several slots for audio users are used for the video users. Fig. 10 shows the capacity of the user data as a function of the capacity of the video users, assuming that the number of audio users is constant. From Fig. 9 it can be observed that the capacity of the data users decreases in accordance to the increase of the video users capacity, this is because several slots of data users are used for video users.
60
User data Capacity
Fig.8 Capacity of audio users a function of the capacity of data users in a multiclass system for Kt = 2, Kr = 2;4, with sectorization and power control.
60
Kt = 2,Kr = 4 50
Fig. 8 to 10 shows that the audio, data and video users capacity decrease as the power control grows increasingly imperfect. The figures also show that as the sectorization grows increasingly imperfect, the audio, data and video users capacity decrease. The effect of beamforming antenna for sectorization can be observed from Fig 8 to 10, where it is shown that the capacity of the audio, data and video users is higher for Kt = 2, Kr = 4 compared to Kt = 2, Kr = 2.
User Data Capacity
ω = 0o ω = 20o 40
σ = 0dB 30
σ = 8dB
20
10
Kt = 2,Kr = 2 0 0
5
10
15
20
25
30
35
40
User Video Capacity
Fig.10 Capacity of data users a function of the capacity of video users in a multiclass system for Kt = 2, Kr = 2;4, with sectorization and power control.
In Fig. 8 to 10 it is shown that the capacity of audio users is higher than the capacity of data and video users, and the
JOURNAL OF TELECOMMUNICATIONS, VOLUME 5, ISSUE 1, OCTOBER 2010 21
capacity of data users is higher than the capacity of the video users. This is due to the fact that the audio processing gain is larger than that of data and video, whilst the data processing gain is larger than that of video, and the lower processing gain means higher bit rate. Higher bit rates require higher power requirements, since power requirement is directily proportional to bit rate, so that the interference signal increases and the capacity decreases. By using sectorization with beamforming antennas, it is shown that the capacity of audio, data and video users in Fig. 8 to 10 is larger compared to system without beamforming as shown in Fig. 2 to 4.
5
CONCLUSIONS
An analysis of multiclass CDMA system with power control and sectorization using beamforming antenna have been done. Results show that: 1. Sectorization using beamforming antenna yields higher multiclass system capacity compared to systems without sectorization. 2. Imperfect sectorization with beamforming can increase the capacity of a multiclass system. 3. The capacity of a multiclass system will increase in accordance to the increased number of the beamforming receive antenna elements in BS while the number of the beamforming transmit antenna elements in MS remains the same. Increasing the number of beamforming receive 4. antenna elements in BS and transmit antenna elements in MS does not always increase the capacity of a multiclass system. The increase of the system capacity is instead due to the distribution of the number of receive antenna elements in BS and transmit antenna elements in MS. The optimum system capacity is attained when the number of receive antenna elements Kr is even. 5. Sectorization using beamforming antennas shows that the capacity for audio, data and video user is higher compared to a system without beamforming antennas.
REFERENCES [1]
[2]
[3]
[4]
K. S. Gilhousen, I. M. Jacobs, R. Padovani, A. J. Viterbi, L.A. Weaver Jr., and C. E. Wheatly III, “On the capacity of a CDMA system,” IEEE Trans on Veh. Technol., vol. 40, no. 2, pp. 303–312, Mei 1991. R. Prasad, M.G. Jansen, A.Kegel, “Capacity Analysis of Cellular Direct Sequence Code Division Multiple Access System With Imperfect Power Control”, IEICE TRANS .COMMUN, Vol.E76-B, No.8, Agustus 1993. Jie Zhou,Y.Onozato,U.Yamamoto,” On the Capacity and Outage Probability of a CDMA Hierarchical Mobile System with Perfect/Imperfect Power Control and Sectorization”, IEICE TRANS FUNDAMENTALS, Vol.E82-A,No.7, July 1999. Juan M. Romero-Jerez, C.Tellez-Labao, A.Diaz-Estrella,”Effect of Power Control Imperfections on the Reverse Link of Cellular CDMA Networks Under Multipath Fading”, IEEE Trans on Veh. Technol., vol. 53, no.1, Januari 2004.
[5]
Jin Yu, Yu-Dong Yao, Jinyun Zhang, “ Reverse-Link Capacity of PowerControlled CDMA Systems With Beamforming”, IEEE Trans on Vehicular Tech, Vol 53, No.5, September 2004. [6] Theodore S. Rappaport, “ Wireless communication : Priciples and practice”, New Jersey: Prentice Hall, 1996. [7] Jhong s.Lee,Leonard E.Miller, “CDMA system engineering handbook”, Boston:Artech House 1998. [8] R. Prasad, “ CDMA for Wireless Personel Communications”, Boston: Artech House,1996. [9] Warren L.Stutsman, Gary A.Thiele,”Antenna Theory and Design”, John Wiley& Sons.Inc,1998. [10] C.A.Balanis,”Antena Theory Analysis and Design”, John Wiley&Sons.Inc,1997. [11] Litva John, T.Kwok,Yeung Lo,” Digital Beamforming in Wireless Communications”, Boston: Artech House,1996. [12] Duk Kyung Kim,”Capacity Estimation for an SIR-Based Power-Controlled CDMA System Supporting ON-OFF Traffic,”IEEE Transaction On Vehicular Technology, Vol.49,No.4 Jui 2000. Gunawan Wibisono was born in Tegal, Indonesia in 1966. He received B.E. degree in electrical engineering from University of Indonesia,Indonesia in 1990, and the M.Sc and Ph.D degrees from Keio University, Japa in telecommunication engineering in 1995 and 1998, respectively. In 1991, he joined Department of Electrical Engineering, Faculty of Engineering University of Indonesia, where he is currently as lecturer and researcher. His current research interest included coding and modulation, electronic communications, wireless communication, and telecommunication regulation. Lina Oktaviana Sari. She received MEng degree from University of Indonesia, Indonesia in electrical engineering in 2007. In 2008, she joined Department of Electrical, Jakarta State Polytechnic, in Indonesia.
